The public service broadcaster committed a "major breach" of media regulations by not revealing that the voice of a film about the Gaza conflict was the offspring of a Hamas administrator, as determined by regulatory body Ofcom.
An investigation by Ofcom into Gaza: How to Survive a Warzone has concluded that the film was "significantly deceptive".
The BBC's director general had already issued an apology, saying there had been "a major oversight in relation to truthfulness".
The authority has directed the corporation to transmit a peak-time declaration about its conclusions.
"Given this constitutes a serious breach of our regulations, we are instructing the broadcaster to air a statement of our determinations against it on the BBC's second channel at 9pm, with a date to be finalised," the regulator stated.
'Risk to Erode Confidence'
The authority's report said: "Our investigation concluded that the programme's lack of disclosure that the voice's parent served in a role in the Hamas-controlled administration was materially misleading.
"It meant that the audience did not have vital facts which may have been highly relevant to their evaluation of the presenter and the content he shared.
"Confidence is at the heart of the bond between a television network and its public, especially for a state-funded media outlet such as the public broadcaster.
"This error had the potential to erode the significantly high amounts of credibility that viewers would have placed in a documentary produced by the BBC about the Israel-Gaza war."
The programme was removed from the online platform in February after the boy's personal associations came to light, and in July an internal BBC review concluded it violated the broadcaster's content policies on accuracy.
A corporation official said: "The authority's determination is in line with the findings of Peter Johnston's review, that there was a major oversight in the programme in relation to the BBC's Editorial Guidelines on truthfulness, which aligns with regulation 2.2 of the authority's broadcasting regulations.
"We have apologised for this and we comply with the regulator's ruling in complete. We will comply with the penalty as soon as the timing and wording are confirmed."
